With the vertex of the known angle A as the center and any value R as the radius, the ratio of the arc length of the angle A to R is a fixed value (independent of R), and we call the positive angle of =R an angle of 1 radian. The angle is measured in units of 1 radian angle. This measuring system is called radian system to show the difference with another angle measuring system-angle system.
The basic idea of arc system is to make the radius and circumference of a circle have the same measurement unit, and then measure the angle by the ratio of the corresponding arc length to the radius of the circle. The prototype of this idea originated in India. The famous Indian mathematician Aliyepito (476)? -550? The circumference of a circle is 2 1600 minutes, and the radius of a circle is 3438 minutes (that is, pi is 3. 142), but Aliyepito did not explicitly put forward the concept of radian system. The strict concept of radian was put forward by the Swiss mathematician Euler (1707- 1783) in 1748. Euler is different from Aliyepito in that the radius is 1 unit, so the arc length of the semicircle is π, and the sine value at this time is 0, so it is recorded as sinπ= 0. Similarly, the arc length of the circumference of 1/4 is π/2, and the sine at this time is 1, so it is recorded as sin (π/2) = 6544. Thus, the central angles of semicircle and 1/4 arc expressed by π and π/2 respectively are established. Other angles can also be analogized.
A radian angle: the angle of the center of an arc with a long radius is called 1 radian angle.
1 radian is approximately equal to 57.3.
It is about 57 17' 45 ".
But it is exactly equal to 180/π.
180 =π radian
The formula of the sector area is S= 1/2LR, where l is the arc length of the sector and r is the radius of the circle.